
Thus, one can interpret prior (3) as \(\sigma _{ij}=0\)  if \(z_{ij}=0\)  with probability \(1-q\)  and \(\sigma _{ij}\sim \text{N}(\cdot |0,v^2)\)  if \(z_{ij}=1\)  with probability \(q\)  for \(i<j\) . Hence, \(\mathcal {Z}\)  can be seen as a covariance structure indicator, or equivalently a graphical structure indicator, following the terminology used by [1]}. Note \(q\)  is the edge acceptance probability; and the larger \(q\)  is, the less model becomes sparse. We may choose not too small \(q\)  and \(v\)  to avoid the extreme sparsity of the model. Compared to the prior in [2]}, our prior naturally introduces sparsity to the structure of model with the point-mass at zero. Define the set
\(\mathcal {U}(\tau )=\lbrace \mathcal {C}\in \mathcal {M}^+: 1/\tau \le \lambda _{\min }\left(\mathcal {C}\right)\le \lambda _{\max } \left(\mathcal {C}\right) \le \tau \rbrace ,\) 
